A bifurcation construction method and system of a cloverleaf orbit family in a earth-moon three-body system

Abstract

The application discloses a bifurcation construction method, system, equipment, medium and program of a clover orbit family in a geolunar three-body system, and belongs to the technical field of aerospace. The method comprises the following steps: constructing a geolunar circular restricted three-body dynamics model according to a geolunar three-body system; obtaining a halo orbit family based on the geolunar circular restricted three-body dynamics model; positioning a halo orbit family bifurcation point, and constructing a transition orbit; obtaining a first clover orbit based on the transition orbit, and extending to obtain a clover orbit family. The application can obtain complex periodic orbit families derived near the libration points L1 and L2 in a restricted three-body system, and quickly constructs the periodic orbit family.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, specifically to a method, system, device, medium, and program for constructing a bifurcation of a cloverleaf orbital family of the Earth-Moon tribody system. Background Technology

[0002] The Earth-Moon space, as a crucial region connecting the Earth and the Moon, has gradually become a new focus of scientific research and commercial activities in recent years with the deepening of space exploration. Within the Earth-Moon space exists a unique dynamic system—the Earth-Moon circular restricted three-body system. This system consists of the Earth, the Moon, and a third object (such as a space station or satellite), which is subject to the combined gravitational influence of both the Earth and the Moon, exhibiting a complex state of motion.

[0003] In the Earth-Moon circular restricted three-body system, there are five special translational points known as Lagrangian points. Among them, translational points L1 and L2 have received widespread attention due to their unique strategic significance and orbital characteristics. Translational point L1 is located between the Earth and the Moon, on the Earth-facing side, and is a point where the gravitational forces of the Earth and the Moon are in equilibrium. At translational point L1, a third object can achieve a relatively stationary state, providing an ideal platform for communication, observation, and other missions between the Earth and the Moon. Translational point L2, on the extended line connecting the Earth and the Moon, on the Earth-remote side, also possesses special gravitational equilibrium characteristics.

[0004] Due to the unique characteristics of multibody dynamics, various types of periodic orbits arise near translational points L1 and L2. Compared to the traditionally widely used halo and DRO orbits, these complex-configured periodic orbits in Earth-Moon space have broader application prospects and strategic value. However, effectively locating and acquiring these periodic orbits, and rapidly constructing them, are problems that need to be solved. Summary of the Invention

[0005] To address the problem in existing technologies of how to obtain complex period-doubling orbits derived near translation points L1 and L2 in a restricted three-body system and to rapidly construct this family of periodic orbits, this invention provides a bifurcation construction method for a cloverleaf orbit family in an Earth-Moon three-body system, enabling the rapid acquisition of this orbit family.

[0006] To achieve the above objectives, the present invention provides the following technical solution.

[0007] In a first aspect, the present invention provides a method for constructing a bifurcation of a cloverleaf orbital family in an Earth-Moon tribody system, comprising:

[0008] Based on the Earth-Moon three-body system, construct a circular restricted three-body dynamic model of the Earth and the Moon;

[0009] Based on the Earth-Moon circular restricted three-body dynamics model, the halo orbital family is obtained;

[0010] Locate the bifurcation point of the halo orbit family and construct the transition orbit;

[0011] The first four-leaf clover orbit was obtained based on the transition orbit, and the four-leaf clover orbit family was obtained by extension.

[0012] As a further improvement of the present invention, the construction of the Earth-Moon circular restricted three-body dynamic model based on the Earth-Moon three-body system is, in the circular restricted three-body problem, the normalized dynamic equations of the spacecraft in the coordinate system are expressed as follows:

[0013]

[0014] In the formula, This represents the effective potential of the Earth-Moon tribody system.

[0015] As a further improvement of the present invention, the method of obtaining the halo orbital family based on the Earth-Moon circular restricted three-body dynamics model includes:

[0016] Based on the Earth-Moon circular restricted three-body dynamics model, the initial value of the halo orbit of the translation point L2, located on the side furthest from Earth on the extension of the line connecting Earth and Moon, in the Earth-Moon three-body system is calculated.

[0017] The family of halo orbits for translational point L2 is obtained based on the natural parameter continuation method.

[0018] As a further improvement of the present invention, the method of locating the bifurcation point of the halo orbital family and constructing the transition orbit includes:

[0019] Obtain the halo orbit family of the translational point L2 in the halo orbit family;

[0020] Based on the Broucke diagram, locate the third four-period bifurcation point in the halo orbit family with a frequency ranging from low to high in the translational point L2.

[0021] The orbital period of the translational point L2halo corresponding to the third four-times period bifurcation point is adjusted to four times. Then, the transition orbit is obtained using the time-fixed differential correction method.

[0022] As a further improvement of the present invention, the method of obtaining the solution to the first four-leaf clover orbit based on the transition orbit includes:

[0023] The solution direction for the new orbit family is determined based on the orbit state of the transition orbit, and the solution is iteratively obtained to obtain the first bifurcation clover orbit.

[0024] As a further improvement of the present invention, the step of obtaining the first four-leaf clover orbit based on the transition orbit and extending it to obtain a family of four-leaf clover orbits includes:

[0025] The first four-leaf clover orbit was extended using the natural parameter extension method to obtain the complete family of four-leaf clover orbits.

[0026] Secondly, the present invention provides a bifurcation structure system for the cloverleaf orbital family of the Earth-Moon tribody system, comprising:

[0027] The dynamic model construction module is used to construct a circular restricted three-body dynamic model of the Earth and the Moon based on the Earth-Moon three-body system.

[0028] The module for obtaining the halo orbital family is used to obtain the halo orbital family based on the Earth-Moon circular restricted three-body dynamics model.

[0029] Transitional track construction module: used to locate the bifurcation points of the halo track family and construct transitional tracks;

[0030] The module for obtaining the four-leaf clover orbit family is used to obtain the first four-leaf clover orbit based on the transition orbit and to extend it to obtain the four-leaf clover orbit family.

[0031] Thirdly, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the bifurcation construction method for a tetrahedral orbital family of the Earth-Moon tribody system.

[0032] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the bifurcation construction method for a tetrahedral orbital family of the Earth-Moon tribody system.

[0033] Fifthly, the present invention provides a computer program product, characterized in that it includes computer instructions, which, when executed by a processor, implement the steps of the bifurcation construction method for the four-leaf clover orbital family of the Earth-Moon tribody system.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The cloverleaf orbit family constructed in this invention provides four-way lunar coverage compared to the unidirectional coverage of NRHO (Nearly Straight Halo Orbit) and DRO (Due Point Orbit) orbits. This means that starting from a cloverleaf orbit, multiple regions of the Moon can be covered more easily without obstruction, which is crucial for missions such as lunar exploration, resource development, and scientific experiments. Furthermore, compared to the DRO orbit family, the cloverleaf orbit family has a higher Jacobian constant and therefore lower orbital energy. This indicates that reaching this orbit family is less costly, which is beneficial for improving mission efficiency and reducing costs. Weak stability means that the orbit can quickly recover to its original state after being subjected to small disturbances, which is crucial for long-term stable orbit maintenance and orbit transfer missions. In addition, the weak stability of the orbit also means that transferring spacecraft into or out of this orbit does not require extremely high fuel consumption. In summary, the weak stability characteristics of the cloverleaf orbit family make it very suitable for long-term missions such as lunar-Earth space shuttle transportation and lunar-Earth space situational awareness. It is evident that constructing a new periodic orbit family through bifurcation methods provides more choices and flexibility for future lunar-Earth space missions. The cloverleaf orbital family designed in this invention is not only applicable to orbit transfer and orbit maintenance missions, but can also be extended to other Earth-Moon space missions, such as Earth-Moon space navigation constellations and Earth-Moon space situational awareness missions. It can also indirectly or directly support lunar orbital rendezvous and docking, lunar base construction and maintenance. This provides support for the diversity and complexity of Earth-Moon space missions.

[0036] Furthermore, the orbital family obtained by this invention is derived from the third four-times-period bifurcation of the halo orbital family at the Earth-Moon translation point L2. Some orbitals in this family possess excellent characteristics such as low orbital energy, critical orbital stability, and four-way lunar coverage, exhibiting significant potential application value. In addition, the bifurcation construction method for multiple-times orbital families proposed in this invention can also be extended to the construction of other types of three-body systems, various basic orbital families, and arbitrary-times-multiple orbital families. Attached Figure Description

[0037] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way. In the drawings:

[0038] Figure 1 This is a schematic diagram illustrating the specific process of a bifurcation construction method for a cloverleaf orbital family in an Earth-Moon tribody system according to the present invention.

[0039] Figure 2 This is a schematic diagram illustrating the bifurcation construction method of a cloverleaf orbital family for the Earth-Moon tribody system according to the present invention.

[0040] Figure 3 A schematic diagram of the southern halo orbital family of the Earth-Moon translation point L2;

[0041] Figure 4 The Broucke curve corresponding to the southern halo orbit of the Earth-Moon translation point L2;

[0042] Figure 5 This serves as a transitional orbit and the first four-leaf clover track after the third four-times-period bifurcation.

[0043] Figure 6 A schematic diagram of the orbital family of the Southern Clover;

[0044] Figure 7 A schematic diagram of the orbital family of the Northern Clover;

[0045] Figure 8 Stability index curves for the North / South Clover orbital family;

[0046] Figure 9 The perilunar / apexarar distance curves for the North / South Clover orbital families;

[0047] Figure 10 Jacobian constant curves for the South / North Clover Orbital Family;

[0048] Figure 11 Jacobian constant curves for the DRO orbital family;

[0049] Figure 12 Jacobian constant curves for the halo orbital family and its NRHO orbital family;

[0050] Figure 13 Track diagrams for a single four-leaf clover track, DRO track, and NRHO track;

[0051] Figure 14 To adjust the orbital period T = The 19.63-day four-leaf clover orbit is converted to the trajectory of three periods under the ephemeris model. Detailed Implementation

[0052] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0053] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0054] The problem that needs to be solved is how to obtain the periodic orbits derived from the translation point L1 and the translation point L2 in the existing technology, and how to quickly construct the periodic orbits. This invention provides a method for constructing the bifurcation of the cloverleaf orbit family in the Earth-Moon tribody system, such as... Figure 1 As shown, the method is as follows:

[0055] Based on the Earth-Moon three-body system, construct a circular restricted three-body dynamic model of the Earth and the Moon;

[0056] Based on the Earth-Moon circular restricted three-body dynamics model, the halo orbital family is obtained;

[0057] Locate the bifurcation point of the halo orbit family and construct the transition orbit;

[0058] The first four-leaf clover orbit was obtained based on the transition orbit, and the four-leaf clover orbit family was obtained by extension.

[0059] The present invention provides a method for constructing a bifurcation of a family of clover-shaped orbits in a restricted three-body system with a lunar-Earth shape. This method can quickly obtain orbits, which have the characteristics of low energy, critical stability, and good coverage.

[0060] The present invention will be further explained below with reference to the accompanying drawings.

[0061] like Figure 2 As shown, this invention proposes a bifurcation construction method for a family of clover-shaped orbits in a restricted three-body system with a lunar-Earth orientation, comprising:

[0062] S1: Calculate the first halo orbit in the family of halo orbits of the translation point L2;

[0063] First, establish a descriptive coordinate system and a rendezvous coordinate system for the Earth-Moon circular restricted three-body problem. The origin of the rendezvous coordinate system is located at the Earth-Moon mass center. x The axis starts from the Earth and points towards the Moon; z The axis represents the direction of the angular velocity of the moon's motion. y shaft and x shaft and z The axes form a right-handed coordinate system. Let the spacecraft state be represented as... In the circular restricted three-body problem, the normalized dynamic equations of the spacecraft in the coordinate system are as follows:

[0064] (1)

[0065] In the formula, Ω3 is the effective potential of the Earth-Moon tri-body system; x , y , z The position of the spacecraft in the rendezvous coordinate system. These represent the spacecraft's velocities in the y-coordinate system and the y-coordinate system, respectively.

[0066] Effective potential of the Earth-Moon tri-body system The expression is:

[0067] (2)

[0068] in, The mass coefficient of the circularly restricted three-body system is expressed as follows:

[0069] (3)

[0070] in, m 1 represents the mass of a relatively large celestial body, while m 2 represents the mass of a relatively small celestial body; for example, the Earth-Moon system. m 1 is the mass of the Earth, and m 2 represents the mass of the Moon. Furthermore, r 1 and r 2 represents the distance from the spacecraft to the Earth and the Moon, respectively, and its expression is:

[0071] (4)

[0072] The system contains five translational points, L1 to L5. For the L2 translational point, for the Earth-Moon system, μ =0.01216, its coordinate value X L2 = [1.157,0,0] T .

[0073] The initial values ​​of the halo trajectory near the translation point can be determined using the Richardson solution, which is written in the local coordinate system of the translation point and its expression is as follows:

[0074] (5)

[0075] In the formula, The motion state of the spacecraft in the translational point coordinate system.

[0076] Taking the Earth-Moon translation point L2 as an example, the translation point coordinate system and the rendezvous coordinate system have the following transformation relationship:

[0077] (6)

[0078] in, The state is in the translational point coordinate system. For the translational point L2 in the coordinate system x coordinate, This is the distance from the translational point L2 to the moon.

[0079] Furthermore, in equation (5), For orbital motion phase, A x , A z In the translational point coordinate system and The amplitude of motion in the direction, and all other parameters are constant coefficients, which can be obtained from the mass coefficient. μ The only certainty.

[0080] The initial values ​​of the halo orbit in the translational point coordinate system can be obtained from the Richardson solution. Transforming this to the rendezvous coordinate system of the restricted three-body system yields the initial values ​​of the halo orbit in the rendezvous coordinate system. Let the halo orbit be a southern family, i.e. Orbit amplitude in translational point coordinate system A z =0.045, after transformation by equation (6), we can obtain xoz The initial state of the orbit on the plane, its specific value rounded to four decimal places.

[0081] (7)

[0082] Subsequently, a time-invariant differential correction method is employed to obtain the exact solution under the restricted three-body model to ensure convergence. Since the initial orbital value is located at... xoz On the plane of symmetry, the control variable of the halo orbit can be set as follows: ,in T For the orbital period, the trajectory is required to pass perpendicularly after half a cycle. xoz The plane. Therefore, the constraint equations are:

[0083] (8)

[0084] Based on Newton's iterative method for multivariable functions, we have the iterative solution expression for nonlinear algebraic equations:

[0085] (9)

[0086] in, This is the result of the previous iteration. The value will be calculated for the next iteration. The Jacobian matrix representing the constraints with respect to the variables to be determined is in The value at that location, This represents the value of the current constraint equation.

[0087] Therefore, by expanding the Jacobian matrix in equation (9), we can obtain the specific iterative format for calculating the halo orbit:

[0088] (10)

[0089] in, State transition matrix The Middle k The first in the row l Each component. Subscript 0 represents the first halo orbit. Set the iteration termination condition. .

[0090] Based on the initial conditions corresponding to equation (7), and according to the iterative equation (10), the exact halo orbital solution can be obtained, and its specific value after rounding to four decimal places is...

[0091] (11)

[0092] S2: When the control variables of the first halo track are obtained based on the above method... X After 0, natural parameters are used to obtain the complete orbital family.

[0093] For the halo orbit of the translation point L2, the natural parameter continuation method is used for continuation. The basic idea is to use the previous exact solution as the initial value, adjust and fix the orbital period of the next orbit, and then use a time-fixed differential correction method for solution. Therefore, the iterative format of the halo orbit in one continuation step is:

[0094] (12)

[0095] Among them, superscript j For the first j Each iteration step, index i The number of halo family members calculated during the extension process i Extended track. T i This is the currently set orbital period. The initial value for the iteration is set to... .

[0096] Based on the above process, the complete halo orbital family can be obtained. X i ( i = 1,2,3,…, N ), that is, there exists within the current orbital family. NA halo orbit. The corresponding family of halo orbits south of the translational point L2 is as follows: Figure 3 As shown.

[0097] S3: Solve for the single-valued matrix of each orbital in the orbital family. M And then solve for the stability parameters based on them. α and β .

[0098] Specifically, single-valued matrix M It is the state transition matrix of the motion state after one period of the periodic orbit with respect to the initial motion state. It is a 6×6 matrix, and its solution expression is:

[0099] (13)

[0100] in, t 0 represents the initial moment of the periodic orbit. T For orbital period. S ( t 0) and S ( t 0+ T These represent the initial orbital state and the orbital state after one cycle of motion, respectively.

[0101] Stability parameters α and β The calculation formula is:

[0102] (14)

[0103] in, Tr The trace represents the matrix, which is the sum of the elements on the main diagonal of the matrix.

[0104] For each halo orbital in the orbital family obtained in step S2, the first orbital is calculated according to equation (14). i The stability coefficients of the single-valued matrix corresponding to each halo orbital. α i and β i and will α As the horizontal axis, β Plotted as the vertical axis in a Broucke diagram, as follows: Figure 4 As shown in the figure, the solid black line represents the stability curve of the halo orbit family at translation point L2. In addition, there are several other bifurcation curves with different line shapes. The intersections of the stability curves and these bifurcation curves are represented by pentagrams, indicating that the halo orbit at translation point L2 may undergo corresponding types of bifurcation at the intersection points.

[0105] Specifically, for cloverleaf orbits, we should focus on the third intersection of the orbit family stability curve and the four-period bifurcation curve. The orbit closest to this intersection is considered the basic bifurcation orbit, and its state is denoted as... Its specific value after rounding to four decimal places is

[0106] (15)

[0107] Subsequently, a transition orbit was constructed based on this orbit.

[0108] S4: The orbits corresponding to the four-fold bifurcation points of the identified halo orbital family are renumbered by a factor of four, and transition orbits are constructed using a time-fixed differential correction method. Let the set of free variable states of the identified halo orbits be... The orbital period of the transition orbit is fixed at 1. Subsequently, the initial state of the transition trajectory is corrected using the time-fixed differential correction algorithm of equation (12) in step S2, resulting in the accurate initial state of the transition trajectory. Its specific value after rounding to four decimal places is

[0109] (16)

[0110] S5: Orbital state based on transition orbit Determine the solution direction for the new orbital family, iterate through the solution, and obtain the first bifurcation clover orbit.

[0111] First, obtain the periodic orbit constraints. F Regarding the initial value of the transition track accuracy The Jacobian matrix has

[0112] (17)

[0113] in,

[0114] (18)

[0115] Therefore, the specific expression for the Jacobian matrix can be written.

[0116] (19)

[0117] Its specific value after rounding to four decimal places is

[0118] (20)

[0119] For D F Singular value decomposition of (X) yields: The specific value after rounding to four decimal places is...

[0120] (twenty one)

[0121] Where S is a 3 × 4 dimensional singular value matrix, V * represents the transpose of the right singular matrix, which is 4 × 4 dimensional. If the defined bifurcation point is sufficiently precise, then the matrix... S The second-to-last singular value is sufficiently close to 0. Therefore, select... V *The second-to-last column vector in the matrix represents the extension direction of the four-leaf clover orbital family, denoted as Δ. X c ,have

[0122] (twenty two)

[0123] S6: This step will solve for the four-leaf clover track after the first bifurcation.

[0124] First, based on the initial state of the transition orbit... X transit and the extension direction Δ of the four-leaf clover track X c,0 To determine the initial values ​​for solving the first four-leaf clover orbit, we have:

[0125] (twenty three)

[0126] in, subscript c Representing a four-leaf clover track, c The number after represents the first p The track has 0, which represents the initial track. (Superscript) j Represents the first step in the solution process j In the next iteration, the initial value is recorded as 0. δ S The step size increment along the extension direction is preferably set to 5×10⁻³.

[0127] Similar to solving for the constraints of halo orbits or cloverleaf orbits, the constraints of cloverleaf orbits should also be related to... xoz Plane symmetry. Therefore, a fundamental periodic symmetry constraint is:

[0128] (twenty four)

[0129] Furthermore, since the bifurcation point iteration process is extremely sensitive, the convergent solution may jump between the original transition trajectory solution and the new four-leaf clover trajectory. Therefore, an additional constraint should be introduced to ensure that the solution iteration process proceeds along the direction of the four-leaf clover trajectory, i.e.

[0130] (25)

[0131] Therefore, the augmented constraint equations can be written as follows:

[0132] (26)

[0133] Therefore, it is possible to construct about The iterative solution expression,

[0134]

[0135] Iterate until It can be assumed that the iteration converges, and the first four-leaf clover orbit after the bifurcation is obtained. For example... Figure 5 As shown, the dashed line represents the transition track, and the solid line represents the first bifurcation clover track obtained based on this.

[0136] The orbital state of the first bifurcation clover track obtained from the solution is given, with the value rounded to four decimal places.

[0137] (27)

[0138] S7: Solve the family of four-leaf clover orbits based on the extension of the first four-leaf clover orbit.

[0139] The cloverleaf orbital family can be extended using the natural parameter extension method, with the extension direction being the frequency decrease direction. The frequency of the first orbital is determined using the following method:

[0140]

[0141] Subsequently, the frequency was gradually reduced to obtain the corresponding orbital period, in order to... p Using the state of the previous four-leaf clover orbit as the initial value, new four-leaf clover orbits are obtained according to the time-fixed differential correction method in step S1. This extension continues until the iteration no longer converges, thus obtaining the complete family of four-leaf clover orbits. For this example, the southern family of four-leaf clover orbits obtained from the southern family halo orbit bifurcation at translation point L2 has the following orbital family curve: Figure 6 As shown. Furthermore, based on the northern halo orbital family of the translational point L2, the northern clover orbital family can also be obtained, and its orbital family curve is shown in... Figure 7 As shown.

[0142] Figure 8 Another way to express the stability coefficients of the four-leaf clover orbital family is given, and its stability coefficient expression is as follows:

[0143] (28)

[0144] in, v q It is a single-valued matrix M eigenvalues, q = 1, 2, 3. If all stability indices... If any stability index is true, then the orbit is linearly stable and has a stable subspace; if any stability index is true, then the orbit is linearly stable and has a stable subspace. If so, the orbit is unstable. Figure 8 Stability curves for the four-leaf clover orbital family are presented. It can be seen that the stability coefficients of all orbitals within the family remain around 1, indicating that the orbitals possess weak stability.

[0145] Figure 9 This shows the perigee and apogee distances of the Cloverleaf Orbiter family. Based on the perigee distance, most orbits in the family will not collide with the Moon.

[0146] Figure 10 , Figure 11 and Figure 12 Jacobian constants for the four-leaf clover orbital family, the DRO orbital family, the halo orbital family, and a portion of the NRHO orbital family are given. C The calculation formula is

[0147] (29)

[0148] The relationship between Jacobi and orbital energy is: the higher the Jacobi constant, the lower the orbital energy. Therefore, in comparison... Figure 10 and Figure 11 as well as Figure 12 From the NRHO portion corresponding to the solid line, it can be observed that, overall, the cloverleaf orbital family has a higher Jacobian constant than the DRO and NRHO orbitals, thus having lower orbital energies and being more suitable for low-energy transfer.

[0149] Figure 13 The trajectory diagrams of the four-leaf clover orbit, DRO orbit, and NRHO orbit are presented. It can be seen that the proposed four-leaf clover orbit exhibits four-directional lunar coverage, while the DRO orbit only provides planar coverage, and the NRHO orbit only provides unilateral coverage. This demonstrates that the four-leaf clover orbit possesses better lunar coverage characteristics.

[0150] Figure 14 It is the orbital period T The 19.63-day four-leaf clover orbit is converted into the trajectory of three periods under the ephemeris model. It can be seen that the four-leaf clover orbit still maintains its original orbital shape under the real ephemeris model, indicating that the orbit also exists under the real force model and can be used as an object in practical engineering.

[0151] In summary, the orbital family obtained based on this invention has four-way lunar coverage capability compared to the traditionally used NRHO and DRO orbits. Moreover, this orbit has a higher Jacobian constant, lower orbital energy, and weak stability, making it suitable for orbit transfer and orbit maintenance missions. It also has potential advantages in future missions such as lunar-Earth space-based flight transportation and lunar-Earth space situational awareness.

[0152] The second objective of this invention is to propose a bifurcation structure system for the cloverleaf orbital family of the Earth-Moon tribody system, comprising:

[0153] The dynamic model construction module is used to construct a circular restricted three-body dynamic model of the Earth and the Moon based on the Earth-Moon three-body system.

[0154] The module for obtaining the halo orbital family is used to obtain the halo orbital family based on the Earth-Moon circular restricted three-body dynamics model.

[0155] Transitional track construction module: used to locate the bifurcation points of the halo track family and construct transitional tracks;

[0156] The module for obtaining the four-leaf clover orbit family is used to obtain the first four-leaf clover orbit based on the transition orbit and to extend it to obtain the four-leaf clover orbit family.

[0157] A third objective of this invention is to provide an electronic device comprising a processor, a memory, and a display screen. The memory and display screen are both connected to the processor, such as via a bus. Optionally, the electronic device may further include a transceiver. It should be noted that in practical applications, the transceiver is not limited to a single unit, and the structure of this electronic device does not constitute a limitation on the embodiments of this application.

[0158] The processor can be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. The processor can also be a combination that implements computational functions, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, etc.

[0159] A bus can include a pathway for transmitting information between the aforementioned components. The bus can be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc.

[0160] The memory may be ROM (Read Only Memory) or other types of static storage devices capable of storing static information and instructions, RAM (Random Access Memory) or other types of dynamic storage devices capable of storing information and instructions, or EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited to these.

[0161] The memory stores the application code that executes the solution of this application, and its execution is controlled by the processor. The processor executes the application code stored in the memory to implement the content shown in the foregoing method embodiments.

[0162] A fourth objective of this invention is to provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, performs the aforementioned functions. Figures 1 to 2 The illustrated method embodiments include various processes. For example, a memory may include instructions that can be executed by a processor of an electronic device to perform the described method.

[0163] A computer-readable storage medium can be a tangible device that holds and stores instructions used by an instruction execution device. A computer-readable storage medium can be, but is not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof. Specifically, a computer-readable storage medium can be a portable computer disk, a hard disk, a USB flash drive, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), staging random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory stick, floppy disk, optical disk, magnetic disk, mechanical encoding device, or any combination thereof.

[0164] A fifth objective of this invention is to provide a computer program product comprising computer instructions that, when executed by a processor, implement the above-described... Figures 1 to 2 The various processes of the method embodiments shown can achieve the same technical effect, and will not be described again here to avoid repetition.

[0165] Many embodiments and applications beyond the examples provided will be apparent to those skilled in the art upon reading the foregoing description. Therefore, the scope of this teaching should not be determined by reference to the foregoing description, but rather by reference to the foregoing claims and the full scope of their equivalents. For purposes of completeness, all articles and references, including patent applications and publications, are incorporated herein by reference. The omission of any aspect of the subject matter disclosed herein in the foregoing claims is not intended as a waiver of that subject matter, nor should it be construed as an indication that the applicant has not considered that subject matter as part of the disclosed inventive subject matter.

[0166] The above content provides a further detailed description of the present invention. It should not be construed that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of protection of the present invention as defined by the submitted claims.

Claims

1. A method for constructing a bifurcation of a cloverleaf orbital family in an Earth-Moon tribody system, characterized in that, include: Based on the Earth-Moon three-body system, construct a circular restricted three-body dynamic model of the Earth and the Moon; Based on the Earth-Moon circular restricted three-body dynamics model, the halo orbital family is obtained; Locate the bifurcation point of the halo orbit family and construct the transition orbit; The first four-leaf clover orbit was obtained based on the transition orbit, and the four-leaf clover orbit family was obtained by extension. The aforementioned Earth-Moon three-body system-based circular restricted three-body dynamics model is a normalized dynamic equation for the spacecraft in the coordinate system within the circular restricted three-body problem, specifically expressed as follows: In the formula, The effective potential of the Earth-Moon tribody system; The halo orbital family obtained based on the Earth-Moon circular restricted three-body dynamics model includes: Based on the Earth-Moon circular restricted three-body dynamics model, the initial value of the halo orbit of the translation point L2, located on the side furthest from Earth on the extension of the line connecting Earth and Moon, in the Earth-Moon three-body system is calculated. The family of halo orbits for translational point L2 is obtained based on the natural parameter continuation method. The location of the halo orbit family bifurcation point and the construction of the transition orbit include: Obtain the halo orbit family of the translational point L2 in the halo orbit family; Based on the Broucke diagram, locate the third four-period bifurcation point in the halo orbit family with the translational point L2, where the orbital frequency increases from low to high. The period of the halo orbit of the translation point L2 corresponding to the third four-times period bifurcation point is adjusted to four times. Then, the transition orbit is obtained by using the fixed-time differential correction method. The process of obtaining the first four-leaf clover orbit based on the transition orbit includes: The solution direction for the new orbit family is determined based on the orbit state of the transition orbit, and the solution is iteratively obtained to obtain the first bifurcation clover orbit. The process of obtaining the first four-leaf clover orbit based on the transition orbit, and then extending it to obtain the family of four-leaf clover orbits, includes: The first four-leaf clover orbit was extended using the natural parameter extension method to obtain the complete family of four-leaf clover orbits.

2. A bifurcation structure system for a cloverleaf orbital family in an Earth-Moon tribody system, characterized in that, The bifurcation construction system for a cloverleaf orbital family of an Earth-Moon tribody system is used to implement the bifurcation construction method for a cloverleaf orbital family of an Earth-Moon tribody system as described in any one of claims 1, comprising: The dynamic model construction module is used to construct a circular restricted three-body dynamic model of the Earth and the Moon based on the Earth-Moon three-body system. The module for obtaining the halo orbital family is used to obtain the halo orbital family based on the Earth-Moon circular restricted three-body dynamics model. Transitional track construction module: used to locate the bifurcation points of the halo track family and construct transitional tracks; The module for obtaining the four-leaf clover orbit family is used to obtain the first four-leaf clover orbit based on the transition orbit and to extend it to obtain the four-leaf clover orbit family.

3. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the bifurcation construction method for a tetraclover orbital family of an Earth-Moon tribody system as described in any one of claims 1.

4. A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the bifurcation construction method for a cloverleaf orbital family of an Earth-Moon tribody system as described in any one of claims 1.

5. A computer program product, characterized in that, Includes computer instructions that, when executed by a processor, implement the steps of a bifurcation construction method for a cloverleaf orbital family of an Earth-Moon tribody system as described in any one of claims 1.

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